# Principal Components Analysis on overlapping contracts

I am conducting several PCAs on the gas forward curves (months, quarters, seasons, calendars) for hedging purposes which give me some rather reasonable and stable results. However, these contracts overlap with each other, for example: in December the front month contract is a part of both the front quarter contract and front calendar contract. I have often come across analysis conducted on yield curves where contracts overlap as well and nobody mentions it.

We are questioning ourselves about the cleanliness of that procedure and these overlaps. My opinion is that that feature only add more correlation into prices which is not undesired. Any idea/suggestion ? Thanks a lot !

I would do as follows:

A) First do PCA on an arbitrage-free monthly curve (assuming the most granular contract you will use is individual months). To ensure no arbitrages, you will need to drop out certain contracts, I would drop the most illiquid ones. To give you an example, if you are in Dec, you might see Jan, Feb and Mar quoted, but also Q1. In this case, I would use Jan and Feb, and determine the arbitrage-free Mar price by using Q1. In the same spirit, you would then use Q1, Q2 and Q3, and determine Q4 via using the calendar year contract. Doing that for multiple days allows you to do PCA to determine curve dynamics down to the granularity which you have in the market.

B) Once you have determined the principal components of the curve movement, you take the product that you want to hedge and look at the optimal combination of products that you can actually trade in order to work out your hedge.

I think that this way of doing it should avoid spurious results, since the curve that you put into the PCA has been cleanly constructed.

To come back to your example, if you are in Dec, and your optimization suggests a hedge which is in part Jan and in part Q1, then it should be because the PCA suggests that you also need to have some Mar contract in the hedge.

• Thanks for your help! We are using the methodology that you are describing to determine our forward curve. Then, if I understand correctly you would apply the PCA on the following curve in Dec : Jan/Feb/Q2/Q3/Q4/CAL/CAL2 ? Or you would allow March, Q1 and seasons to be included ? Commented Feb 11, 2019 at 9:51
• From the point of view of Dec, I would probably use the following products on my PCA: Jan/Feb/Q1/Q2/Q3/CAL#1/CAL#2. March as least liquid monthly contract to be omitted (is implied out of Q1/Jan/Feb). Q4 also to be omitted (follows from Q1/Q2/Q3/CAL#1)
– ZRH
Commented Feb 11, 2019 at 10:41